48-inch CMP road crossing HDS-5 North Carolina

Culvert inlet vs outlet control: a 48-inch CMP crossing under a county road in Wake County, NC

County maintenance wants to replace a failing crossline before the next subdivision upstream comes online. The question is not just "will the pipe carry 110 cfs?" but whether inlet or outlet control governs — because that sets headwater over the road and whether you need a better entrance or a larger pipe. This walks both HDS-5 checks for a 48-inch CMP with a square-edged headwall.

Result: Design Q = 110 cfs. Outlet-control headwater HW_o/D = 1.05 (≈4.2 ft). Inlet-control headwater HW_i/D = 1.35 (≈5.4 ft). Inlet control governs — improve entrance (type III → type I headwall) or upsize to 54-in CMP. Tailwater TW/D = 0.85 keeps outlet from governing.

Crossing inputs

Parameter	Value	Source
Pipe	48-in CMP, n = 0.024	Existing / proposed standard
Length, L	120 ft	Roadway width + embankment
Slope, S_o	0.020 (2%)	Profile
Entrance	Type III — square edge with headwall	HDS-5 Chart 8
Design discharge, Q	110 cfs	10-yr peak from upstream TR-55 model
Tailwater, TW	3.4 ft (TW/D = 0.85)	Downstream channel depth at Q
Barrel diameter, D	4.0 ft	48-in inside diameter

Step 1 — Outlet control (barrel + tailwater)

Outlet control uses the barrel resistance and downstream tailwater. Manning full-flow capacity (check the pipe is not capacity-limited):

$A = \frac{\pi D^2}{4} = 12.57 \text{ ft}^2, \quad R = \frac{D}{4} = 1.0 \text{ ft}$

$Q_{full} = \frac{1.486}{n} A R^{2/3} S_o^{1/2} = \frac{1.486}{0.024} (12.57)(1.0)^{2/3}(0.02)^{0.5} = 138 \text{ cfs}$

138 cfs > 110 cfs — the barrel can carry the design flow at normal depth. Headwater depth H_o (from HDS-5 outlet nomograph / equation form) with entrance loss k_e = 0.5 and TW/D = 0.85:

$HW_o = H + k_e \frac{V^2}{2g} + TW - S_o L$

At Q = 110 cfs, V = Q/A = 8.75 fps, friction slope ≈ S_o for full flow:

$\frac{HW_o}{D} \approx 1.05 \Rightarrow HW_o = 4.2 \text{ ft}$

Step 2 — Inlet control (entrance geometry)

Inlet control sets headwater independent of barrel friction when the entrance chokes flow. HDS-5 Chart 8 for CMP, headwall, square edge (type III):

$\frac{HW_i}{D} = H_c + \frac{Q}{A \sqrt{2g}} \cdot K_u$

At Q = 110 cfs with K_u = 1.0 (US units), read HW_i/D = 1.35 from the inlet nomograph:

$HW_i = 1.35 \times 4.0 = 5.4 \text{ ft}$

Step 3 — Governing condition

Control	HW/D	Headwater (ft)	Governs?
Outlet	1.05	4.2	No
Inlet	1.35	5.4	Yes

Inlet control governs at 5.4 ft headwater. The county freeboard criterion is 1.0 ft below the road edge (crest elev. 742.0, allowable HW = 741.0). At 5.4 ft above invert (inv = 735.5), HW elev = 740.9 — barely passes. Any rounding or debris knockdown fails.

Step 4 — Fix options

Option	Effect on inlet HW/D	New HW (ft)
Improve entrance to type I (beveled)	1.35 → 1.15	4.6
Upsize to 54-in CMP (same entrance)	1.35 → 1.20	5.4 (D = 4.5 ft)
Lower tailwater (channel improvement)	Outlet may govern instead	Recalculate both

Always run both controls. A pipe sized only on Manning capacity misses inlet-governed headwater — the most common culvert mistake on county roads.

Model the crossing inside the watershed

HydroComplete links the upstream hydrograph to the culvert rating, checks headwater across storm sizes, and keeps the conveyance network in the same project as runoff and detention.

Open in app 14-day free trial

Sources and further reading

FHWA. HDS-5 Hydraulic Design of Highway Culverts. 3rd ed. — inlet and outlet control procedures.
FHWA. HDS-4 Introduction to Highway Hydrology. Design discharge frequency for crosslines.
NCDOT. Hydraulics Unit — standard entrance types and freeboard at county roads.
USDA-NRCS. TR-55 — peak discharge feeding the crossing (referenced, not re-derived here).

— Michael Flynn, PE
Inlet/outlet nomographs in HDS-5 are chart-based; this example uses the equation forms consistent with PE-Calc's culvert tool and HydroComplete's Conveyance engine.

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